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Recent questions tagged calculus

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303
ISI2016-MMA-5
Let $ f(x, y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x, y) \neq (0, 0) \\ 0 & \text{ if } (x, y) = (0, 0) \end{cases}$ Then $\lim_{(x, y) \rightarrow (0,0)}$f(x,y)$ equals $0$ equals $1$ equals $2$ does not exist
Let $ f(x, y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x, y) \neq (0, 0) \\ 0 & \text{ if } (x, y) = (0, 0) \end{cases}$Then $\lim_{(x, y) \rightarrow (0,0)}...
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2 votes
2 answers
304
ISI2016-MMA-8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals$64/5$$32/5$$37/5$$67/5$
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306
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?$0$$\sqrt{\pi}...
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1 votes
1 answer
309
NIELIT2017 STA-set-c-119
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is: Continuous and Differentiable Continuous but not Differentiable Differentiable but not Continuous Neither Continuous nor Differentiable
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is:Continuous and Differentiable Continuous but not DifferentiableDifferentiable but not ContinuousNeither Continuous nor ...
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1 votes
1 answer
311
MadeEasy Test Series: Calculus - Functions
Consider the following function $f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$ ... is defined on $R \rightarrow R-\{ \frac{1}{2} \}$, then it will be a bijection. Please let me know what's correct?
Consider the following function$f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$Is the function a bijection?Yes, this is a one-to-one function.For onto, let's suppose functi...
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1 votes
1 answer
312
Finding Maxima Minima
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____
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0 votes
1 answer
313
Calculus-Self Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
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0 votes
0 answers
314
Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
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0 votes
1 answer
315
Derivative
What is the derivative of the following function at x=0? F(x)= x ^(1/3)
What is the derivative of the following function at x=0?F(x)= x ^(1/3)
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1 votes
1 answer
316
Definite Integral
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$ Please explain how to solve it.
$\displaystyle S = \int_{0}^{2\pi } \sqrt{4\cos^{2}t +\sin^{2}t} \, \, dt$Please explain how to solve it.
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1 votes
1 answer
317
Limit
Puzzle $\lim_{y\rightarrow \alpha }\left (y-\left ( y^{2}+y \right )^{\frac{1}{2}}\right )$
Puzzle$\lim_{y\rightarrow \alpha }\left (y-\left ( y^{2}+y \right )^{\frac{1}{2}}\right )$
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0 votes
0 answers
318
Limits
$\displaystyle\lim_{x \to 0} \left[ \dfrac{log(1+x)}{x} \right] ^{\dfrac{1}{x}} $
$\displaystyle\lim_{x \to 0} \left[ \dfrac{log(1+x)}{x} \right] ^{\dfrac{1}{x}} $
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2 votes
2 answers
319
Limit
Is answer will be 1 or 5? $\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$
Is answer will be 1 or 5?$\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$
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1 votes
1 answer
321
IIT M MS Question
Since given increasing,so $N'(t)>0$ but what will be $N''(t)$ for the slow rate part?
Since given increasing,so $N'(t)>0$ but what will be $N''(t)$ for the slow rate part?
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1 votes
2 answers
322
How Ans. A is correct
At x = 0, the function f(x)=|x| has (A) a minimum (B) a maximum (C) a point of inflection (D) neither a maximum nor minimum
At x = 0, the function f(x)=|x| has(A) a minimum(B) a maximum(C) a point of inflection(D) neither a maximum nor minimum
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0 votes
3 answers
324
Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$
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0 votes
0 answers
325
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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0 votes
0 answers
326
Calculus Integration
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
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5 votes
3 answers
328
ISI2017-MMA-1
The area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x= 0$ and $x=1$ is given by $\frac{\pi}{3}+\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$ $\frac{\pi}{3}-\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{2}$
The area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x= 0$ and $x=1$ is given by$\frac{\pi}{3}+\frac{\sqrt{3}}{2}$$\frac{\pi}{6}+...
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3 votes
3 answers
329
ISRO2018-15
The domain of the function $\log (\log \sin(x))$ is: $0<x<$\pi$ $2n$\pi$<$x$<$(2n+1)$\pi$, for $n$ in $N$ Empty set None of the above
The domain of the function $\log (\log \sin(x))$ is:$0<x<$$\pi$$2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$Empty setNone of the above
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0 votes
1 answer
330
Maths calculus
a)π/√2 B) √π/2 C) π/2 D)√(π/2
a)π/√2 B) √π/2C) π/2 D)√(π/2
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